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 A278477 Primes that set a new record for the Hamming weight. 1
 2, 3, 7, 23, 31, 127, 383, 991, 2039, 3583, 6143, 8191, 63487, 129023, 131071, 522239, 524287, 1966079, 4128767, 14680063, 33546239, 67108351, 201064447, 260046847, 536739839, 1073479679, 2147483647, 8581545983, 16911433727 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Mersenne primes (A000668) are a subsequence. LINKS Robert Israel, Table of n, a(n) for n = 1..3301 MAPLE M:= 40: # to use A061712(1..M) A061712:= proc(n) local d, c, cands;   for d from 0 do     cands:= map(t -> 2^(n+d)-1 - add(2^(n-1+d-j), j=t),         combinat:-choose([\$1..n-2+d], d));     for c in cands do if  isprime(c) then return c fi od   od end proc: A061712(1):= 2: R:= map(A061712, [\$1..M]): R[select(t -> R[t] < `if`(isprime(2^(M+1)-1), 2^(M+1)-1, 2^(M+2)+2^M-1) and R[t] = min(R[t..-1]), [\$1..nops(R)])]; # Robert Israel, Nov 23 2016 PROG (PARI) {my(h=0); forprime(p=2, 10^11, my(t=hammingweight(p)); if(t>h, print1(p, ", "); h=t)); } CROSSREFS Cf. A000668, A061712, A211997. Sequence in context: A236514 A211997 A127581 * A118883 A061712 A059661 Adjacent sequences:  A278474 A278475 A278476 * A278478 A278479 A278480 KEYWORD nonn,base AUTHOR Joerg Arndt, Nov 23 2016 STATUS approved

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Last modified April 23 13:25 EDT 2019. Contains 322386 sequences. (Running on oeis4.)